Purpose: Inverse problems are often marked by highly dimensional state vectors. The high dimension affects the quality of the estimation result as well as the computational complexity of the estimation problem. This paper aims to present a state reduction technique based on prior knowledge. Design/methodology/approach: Ill-posed inverse problems require prior knowledge to find a stable solution. The prior distribution is constructed for the high-dimensional data space. The authors use the prior distribution to construct a reduced state description based on a lower-dimensional basis, which they derive from the prior distribution. The approach is tested for the inverse problem of electrical capacitance tomography. Findings: Based on a singular value decomposition of a sample-based prior distribution, a reduced state model can be constructed, which is based on principal components of the prior distribution. The approximation error of the reduced basis is evaluated, showing good behavior with respect to the achievable data reduction. Owing to the structure, the reduced state representation can be applied within existing algorithms. Practical implications: The full state description is a linear function of the reduced state description. The reduced basis can be used within any existing reconstruction algorithm. Increased noise robustness has been found for the application of the reduced state description in a back projection-type reconstruction algorithm. Originality/value: The paper presents the construction of a prior-based state reduction technique. Several applications of the reduced state description are discussed, reaching from the use in deterministic reconstruction methods up to proposal generation for computational Bayesian inference, e.g. Markov chain Monte Carlo techniques.

Knowledge about the dielectric properties of materials, i.e., the relative permittivity and the conductivity, is important for various sensing applications and engineering. In pneumatic conveying systems, the dielectric properties of the transported good are affected by the transport gas, which aerates the pulverized material, effectively decreasing the permittivity. Traditional probe designs such as the open-ended coaxial probe are well suited for the dielectric characteristics of liquids, gels, and pulverized materials. However, to measure the dielectric properties for aerated materials, the probe has to provide measures to create an aerated state. In this paper, we present a probe design to measure the dielectric properties of aerated pulverized materials. The probe maintains a coaxial design with a dedicated gas injection, enabling the analysis of diluted materials. We discuss the design of the probe, show the modeling of the probe, and present suitable calibration techniques. Furthermore, we analyze the uncertainty of the probe design by means of a statistical analysis of the calibration approach.

Pneumatic conveying is a standard transportation technique for bulk materials in various industrial fields. Flow metering is crucial for the efficient and reliable operation of such systems and for process control. Capacitive measurement systems are often proposed for this application. In this method, electrodes are placed on the conveyor systems transport line and capacitive signals are sensed. The design of the sensor with regard to the arrangement and the number of electrodes as well as the evaluation of the capacitive sensor signals can be divided into two categories. Calibration-based flow meters use regression methods for signal processing, which are parametrized from calibration measurements on test rigs. Their performance is limited by the extend of the calibration measurements. Electrical capacitance tomography based flow meters use model-based signal processing techniques to obtain estimates about the spatial material distribution within the sensor. In contrast to their calibration-based counterparts, this approach requires more effort with respect to modeling and instrumentation, as typically a larger number of measurement signals has to be acquired. In this work we present a comparative analysis of the two approaches, which is based on measurement experiments and a holistic system model for flow metering. For the model-based analysis Monte Carlo simulations are conducted, where randomly generated pneumatic conveying flow patterns are simulated to analyze the sensor and algorithm behavior. The results demonstrate the potential benefit of electrical capacitance tomography based flow meters over a calibration-based instrument design.

Capacitive sensing has become a favourable measurement technology for flow metering in pneumatic conveying systems. Multi electrode sensing structures and tomographic signal evaluations enable spatially resolved flow parameter estimation, which is of particular interest for pneumatically conveyed solids due to inhomogeneous particle distributions within the pipeline. The non-invasive working principle of capacitive sensors is an important feature for the application in industrial processes with harsh environments. However, cross-sensitivities of the capacitive probe cause effects such as temperature drifts of the measurements. For a reliable operation of capacitive flow meters in harsh environments, induced drifts have to be compensated. In this paper we present detailed analyses of thermal effects within capacitive sensors. Based on the findings, a model based temperature compensation approach is developed within the Bayesian framework. The performance of the proposed compensation approach is analysed by a measurement based validation within a climate chamber and by a simulation based uncertainty quantification. The capability to obtain temperature independent estimates with calibration measurements acquired at room temperature is demonstrated.